In this paper, we investigate the influence of the angular momentum of a charged particle on the chaos bound around a charged Einstein-Euler-Heisenberg AdS black hole, and find specific regions where the chaos bound is violated. The black hole is a solution of the Einstein gravity coupled to nonlinear electrodynamics. The Lagrangian of the nonlinear electrodynamics was first constructed by Heisenberg and Euler by using the Dirac electron-positron theory, and reconstructed by Schwinger in the frame of quantum electrodynamics [1]}. Based on the Lagrangian, some interesting solutions of black hole were gotten and their properties were studied [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}. An important feature of the AdS black hole is the existence of the phase transitions and critical phenomenon, where the cosmological constant is regarded as a thermodynamic pressure and its conjugate quantity is a thermodynamic volume. Moreover, recent developments in the AdS/CFT correspondence greatly stimulate the study of the AdS black hole. The Lyapunov exponent is obtained by solving the eigenvalue of a Jacobian matrix in a phase space. The angular momentum plays an important role in the investigation. It affects not only the value of the Lyapunov exponent, but also the position of an equilibrium orbit. By fixing the charge mass ratio and changing the value of the angular momentum, we find the positions of different equilibrium orbits and the specific regions where the chaos bound is violated. The bound is numerically discussed in the near-horizon region and at a certain distance from the horizon.
